New recursions for tree-level correlators in (Anti) de Sitter space

Abstract

We present for the first time classical multiparticle solutions in Anti de Sitter space (AdS) involving scalars, gluons, and gravitons. They are recursively defined through multiparticle currents which reduce to Berends-Giele currents in the flat space limit. This construction exposes a compact definition of tree-level boundary correlators using a general prescription that removes unphysical boundary contributions. Similarly to the flat space perturbiner, a convenient gauge choice leads to a scalar basis for all degrees of freedom, while the tensor structure is exclusively captured by field theory vertices. This provides a fully automated way to compute AdS boundary correlators to any multiplicity and cosmological wavefunction coefficients after Wick-rotating to de Sitter space.

arXiv comment9 pages. v2: references added. v3: published version, with fixed typo in equation (37)

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• Multivariate hypergeometric solutions of cosmological (dS) correlators by $\text{d}\log$-form differential equations
• Flat-space structure of gluon and graviton in AdS
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• Celestial Berends-Giele current
• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• Notes on weight-shifting operators and unifying relations for cosmological correlators
• A Match Made in Heaven: Linking Observables in Inflationary Cosmology
• Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
• Perturbative Unitarity Calls for An Action
• The off-shell expansion relation of the Yang-Mills scalar theory
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• The bi-adjoint scalar $\ell$-loop planar integrand recursion and graded inverse variables